17=2+20t-5t^2

Solution for 17=2+20t-5t^2 equation:

Simplifying
17 = 2 + 20t + -5t2

Solving
17 = 2 + 20t + -5t2

Solving for variable 't'.

Combine like terms: 17 + -2 = 15
15 + -20t + 5t2 = 2 + 20t + -5t2 + -2 + -20t + 5t2

Reorder the terms:
15 + -20t + 5t2 = 2 + -2 + 20t + -20t + -5t2 + 5t2

Combine like terms: 2 + -2 = 0
15 + -20t + 5t2 = 0 + 20t + -20t + -5t2 + 5t2
15 + -20t + 5t2 = 20t + -20t + -5t2 + 5t2

Combine like terms: 20t + -20t = 0
15 + -20t + 5t2 = 0 + -5t2 + 5t2
15 + -20t + 5t2 = -5t2 + 5t2

Combine like terms: -5t2 + 5t2 = 0
15 + -20t + 5t2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(3 + -4t + t2) = 0

Factor a trinomial.
5((1 + -1t)(3 + -1t)) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(1 + -1t)' equal to zero and attempt to solve:

Simplifying
1 + -1t = 0

Solving
1 + -1t = 0

Move all terms containing t to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + -1t = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1t = 0 + -1
-1t = 0 + -1

Combine like terms: 0 + -1 = -1
-1t = -1

Divide each side by '-1'.
t = 1

Simplifying
t = 1
Subproblem 2
Set the factor '(3 + -1t)' equal to zero and attempt to solve:

Simplifying
3 + -1t = 0

Solving
3 + -1t = 0

Move all terms containing t to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + -1t = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1t = 0 + -3
-1t = 0 + -3

Combine like terms: 0 + -3 = -3
-1t = -3

Divide each side by '-1'.
t = 3

Simplifying
t = 3
Solution
t = {1, 3}